Hyperbolic dimension and radial Julia sets of transcendental functions

Rempe, Lasse

doi:10.1090/S0002-9939-08-09650-0

Hyperbolic dimension and radial Julia sets of transcendental functions
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Proc. Amer. Math. Soc. 137 (2009), 1411-1420 Request permission

Abstract:

We survey the definition of the radial Julia set $J_r(f)$ of a meromorphic function (in fact, more generally, any Ahlfors islands map), and give a simple proof that the Hausdorff dimension of $J_r(f)$ and the hyperbolic dimension $\dim _{\operatorname {hyp}}(f)$ always coincide.

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